Eigenvalue decomposition precoding matrix index selection

ABSTRACT

A method and system for selecting precoding matrix index are herein disclosed. The method includes determining a precoder and candidate beams, selecting base beams based on a correlation power between the determined precoder and determined candidate beams, and estimating amplitude coefficients and cophase coefficients by projecting a channel on the selected base beams.

PRIORITY

This application is a Continuation-in-Part Application of, and claimspriority to, U.S. patent application Ser. No. 16/256,301 filed on Jan.24, 2019 and claimed priority under 35 U.S.C. § 119(e) to a U.S.Provisional Patent Application filed on Nov. 21, 2018 in the UnitedStates Patent and Trademark Office and assigned Ser. No. 62/770,326, theentire contents of which are incorporated herein by reference.

FIELD

The present disclosure relates generally to a method and system forselecting precoding matrix indices.

BACKGROUND

Legacy precoding matrix index (PMI) selection methods based on codebooksearch are increasingly impractical due to the large codebook size.Existing implementation usually use greedy search methods to select thePMI which has high complexity, resulting in low performance.

SUMMARY

According to one embodiment, a method is provided. The method includesdetermining a precoder and candidate beams, selecting base beams basedon a correlation power between the determined precoder and determinedcandidate beams, and estimating amplitude coefficients and cophasecoefficients by projecting a channel on the selected base beams.

According to one embodiment, a system is provided. The system includes areceiver, a transmitter, and a processor configured to determine aprecoder and candidate beams, select base beams based on a correlationpower between the determined precoder and determined candidate beams,and estimate amplitude coefficients and cophase coefficients byprojecting a channel on the selected base beams.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features, and advantages of certainembodiments of the present disclosure will be more apparent from thefollowing detailed description, taken in conjunction with theaccompanying drawings, in which:

FIG. 1 is a flowchart for a method of selecting a PMI algorithm/process,according to an embodiment;

FIG. 2 is a diagram of a linear complexity method used to find indices,according to an embodiment; and

FIG. 3 is a block diagram of an electronic device in a networkenvironment, according to one embodiment.

DETAILED DESCRIPTION

Hereinafter, embodiments of the present disclosure are described indetail with reference to the accompanying drawings. It should be notedthat the same elements will be designated by the same reference numeralsalthough they are shown in different drawings. In the followingdescription, specific details such as detailed configurations andcomponents are merely provided to assist with the overall understandingof the embodiments of the present disclosure. Therefore, it should beapparent to those skilled in the art that various changes andmodifications of the embodiments described herein may be made withoutdeparting from the scope of the present disclosure. In addition,descriptions of well-known functions and constructions are omitted forclarity and conciseness. The terms described below are terms defined inconsideration of the functions in the present disclosure, and may bedifferent according to users, intentions of the users, or customs.Therefore, the definitions of the terms should be determined based onthe contents throughout this specification.

The present disclosure may have various modifications and variousembodiments, among which embodiments are described below in detail withreference to the accompanying drawings. However, it should be understoodthat the present disclosure is not limited to the embodiments, butincludes all modifications, equivalents, and alternatives within thescope of the present disclosure.

Although the terms including an ordinal number such as first, second,etc. may be used for describing various elements, the structuralelements are not restricted by the terms. The terms are only used todistinguish one element from another element. For example, withoutdeparting from the scope of the present disclosure, a first structuralelement may be referred to as a second structural element. Similarly,the second structural element may also be referred to as the firststructural element. As used herein, the term “and/or” includes any andall combinations of one or more associated items.

The terms used herein are merely used to describe various embodiments ofthe present disclosure but are not intended to limit the presentdisclosure. Singular forms are intended to include plural forms unlessthe context clearly indicates otherwise. In the present disclosure, itshould be understood that the terms “include” or “have” indicateexistence of a feature, a number, a step, an operation, a structuralelement, parts, or a combination thereof, and do not exclude theexistence or probability of the addition of one or more other features,numerals, steps, operations, structural elements, parts, or combinationsthereof.

Unless defined differently, all terms used herein have the same meaningsas those understood by a person skilled in the art to which the presentdisclosure belongs. Terms such as those defined in a generally useddictionary are to be interpreted to have the same meanings as thecontextual meanings in the relevant field of art, and are not to beinterpreted to have ideal or excessively formal meanings unless clearlydefined in the present disclosure.

The electronic device according to one embodiment may be one of varioustypes of electronic devices. The electronic devices may include, forexample, a portable communication device (e.g., a smart phone), acomputer, a portable multimedia device, a portable medical device, acamera, a wearable device, or a home appliance. According to oneembodiment of the disclosure, an electronic device is not limited tothose described above.

The terms used in the present disclosure are not intended to limit thepresent disclosure but are intended to include various changes,equivalents, or replacements for a corresponding embodiment. With regardto the descriptions of the accompanying drawings, similar referencenumerals may be used to refer to similar or related elements. A singularform of a noun corresponding to an item may include one or more of thethings, unless the relevant context clearly indicates otherwise. As usedherein, each of such phrases as “A or B,” “at least one of A and B,” “atleast one of A or B,” “A, B, or C,” “at least one of A, B, and C,” and“at least one of A, B, or C,” may include all possible combinations ofthe items enumerated together in a corresponding one of the phrases. Asused herein, terms such as “1^(st),” “2nd,” “first,” and “second” may beused to distinguish a corresponding component from another component,but are not intended to limit the components in other aspects (e.g.,importance or order). It is intended that if an element (e.g., a firstelement) is referred to, with or without the term “operatively” or“communicatively”, as “coupled with,” “coupled to,” “connected with,” or“connected to” another element (e.g., a second element), it indicatesthat the element may be coupled with the other element directly (e.g.,wiredly), wirelessly, or via a third element.

As used herein, the term “module” may include a unit implemented inhardware, software, or firmware, and may interchangeably be used withother terms, for example, “logic,” “logic block,” “part,” and“circuitry.” A module may be a single integral component, or a minimumunit or part thereof, adapted to perform one or more functions. Forexample, according to one embodiment, a module may be implemented in aform of an application-specific integrated circuit (ASIC).

The present systems, methods, and devices are targeted at improving thePMI selection accuracy based on eigenvalue decomposition (ED). Thepresent systems, methods, and devices exploit the codebook structure andestimate the PMI based on the correlation between the ideal ED precoderand the PMI candidates.

Disclosed herein is a two-stage PMI selection method. First, the idealprecoder is computed by ED and the base beams indices are selected basedon the correlation power between the ideal ED precoder and all thecandidate beams. Second, the amplitude and cophase coefficients areestimated based on the correlation between the ideal ED precoder and theselected beams. The present systems, methods, and devices reduce EDdimensions to reduce complexity, and they can be applied to any linearcombination structure codebook.

The PMI selection is based on finding the candidate codeword that hashighest correlation power with the ideal ED precoder. In some examples,a correlation based beam selection method is used for the specific beamselection constraints in eFD-MIMO. The amplitude and cophasecoefficients are estimated based on the correlation between ideal EDprecoder and the selected beams.

FIG. 1 is a flowchart 100 for a method of selecting a PMIalgorithm/process, according to an embodiment. At 102, the presentsystem determines an ideal precoder and candidate beams. The idealprecoder may be determined/computed by singular value decomposition(SVD).

The eigenvector of H^(H)H on r-th polarization of the l-th layer of thej-th subcarrier is denoted as v_(r,l,j). The precoding vector on ther-th polarization, l-th layer of the k-th subband is donated asw_(r,l,k). Defining k₁=[k₁ ⁽⁰⁾, k₁ ⁽¹⁾, . . . , k₁ ^((L-1))], k₂=[k₂⁽⁰⁾, k₂ ⁽¹⁾, . . . , k₂ ^((L-1))], p_(r,l,k)=[p_(r,l,0,k), p_(r,l,1,k),. . . , p_(r,l,L-1,k)] and c_(r,l,k)=[c_(r,l,0,k), c_(r,l,1,k), . . . ,c_(1,l,L-1,k)], the precoding vector is set as Equation (1):

$\begin{matrix}{w_{r,l,k} = {{f\left( {k_{1},k_{2},p_{r,l,k},c_{r,l,k}} \right)} = {\sum\limits_{i}{p_{r,l,i,k}c_{r,l,i,k}b_{k_{1}^{(i)}k_{2}^{(i)}}}}}} & (1)\end{matrix}$

with Equation (2):

$\begin{matrix}{{b_{k_{1},k_{2}} = {\left\lbrack {e^{j\frac{2\pi\; k_{1} \times 0}{N_{1}O_{1}}},e^{j\frac{2\pi\; k_{1} \times 1}{N_{1}O_{1}}},\ldots\;,e^{j\frac{2\pi\; k_{1} \times {({N_{1} - 1})}}{N_{1}O_{1}}}} \right\rbrack^{T} \otimes \left\lbrack {e^{j\frac{2\pi\; k_{2} \times 0}{N_{2}O_{2}}},e^{j\frac{2\pi\; k_{2} \times 1}{N_{2}O_{2}}},\ldots\;,e^{j\frac{2\pi\; k_{2} \times {({N_{2} - 1})}}{N_{2}O_{2}}}} \right\rbrack^{T}}}\mspace{79mu}{{where}\mspace{14mu}\left\{ \begin{matrix}{{k_{1} = 0},1,\ldots\;,{{N_{1}O_{1}} - 1}} \\{{k_{2} = 0},1,\ldots\;,{{N_{2}O_{2}} - 1}}\end{matrix} \right.}} & (2)\end{matrix}$

For beam selection, the metric function is defined as Equation (3):

$\begin{matrix}{{J\left( {{\overset{\hat{}}{k}}_{1},{\overset{\hat{}}{k}}_{2}} \right)} = {\sum\limits_{i = 0}^{L - 1}\beta_{i}^{2}}} & (3)\end{matrix}$

with the correlation power defined as Equation (4):

$\begin{matrix}{\beta_{i}^{2} = {\sum\limits_{r}{\sum\limits_{l}{\sum\limits_{j}\rho_{r,l,i,j}^{2}}}}} & (4)\end{matrix}$

and considering Equation (5):

$\begin{matrix}{{\overset{\hat{}}{k}}_{1},{{\overset{\hat{}}{k}}_{2} = {\arg\mspace{11mu}{\max\limits_{k_{1},k_{2}}{J\left( {k_{1},k_{2}} \right)}}}}} & (5)\end{matrix}$

the correlation is defined as ρ_(r,l,i,j)=b_(x) _(i) ^(H)v_(r,l,j), andthe L selected beams are b_(x) ₀ , b_(x) ₁ , . . . , b_(x) _(L-1) .

At 104, the present system selects base beams based on correlation powerbetween the determined precoder and the candidate beams, and 102 may becarried out using part or all of the candidate beams.

For a two-dimensional discrete Fourier transform (2D-DFT) codebook,Equation (6), (7), (8), and (9) are known as:k ₁ ^((i)) =O ₁ n ₁ ^((i)) +q ₁ ,i=0, . . . ,L−1  (6)k ₂ ^((i)) =O ₂ n ₂ ^((i)) +q ₂ ,i=0, . . . ,L−1  (7)q ₁=0, . . . ,O ₁−1,q ₂=0, . . . ,O ₂−1  (8)n ₁ ^((i))=0, . . . ,N ₁−1,n ₂ ^((i))=0, . . . ,N ₂−1  (9)

This indicates that these L beams must have the same frequency rotationfactor (q₁ and q₂). When codebook subset restriction (CBSR) is applied,n₁ ^((i)) and n₂ ^((i)) are restricted to subsets of {0, . . . , N₁−1}and {0, . . . , N₂−1} separately. An example without CB SR is describedbelow, and it could be easily applied by limiting the search space.

Since these L beams always share the same frequency rotation factor q₁and q₂, searching the q values in the beam selection process (fractionalindices selection) can be conducted first. For each candidate pair (q₁,q₂), the L best beams (integer indices selection) are selected anddenoted as b_(x) _(i) (q₁, q₂), i=0, 1, . . . , L−1. The candidate Linteger indices with the maximum correlation metric are selected and theL beams are chosen accordingly.

For each hypothesis of q₁ and q₂, the valid set of precoding vector aredenoted as Equation (10):B′(q ₁ ,q ₂)=(R _(N) ₁ (q ₁)D _(N) ₁ )⊗(R _(N) ₂ (q ₂)D _(N) ₂ )  (10)

where D_(N) is a DFT matrix with size N and R_(N) _(i) (q_(i)) is thefrequency rotation matrix, denoted as Equation (11):

$\begin{matrix}{{{R_{N_{i}}\left( q_{i} \right)} = {{diag}\left( \begin{bmatrix}e^{j\; 2{\pi \cdot 0 \cdot \frac{q_{i}}{N_{i}O_{i}}}} & e^{j\; 2{\pi \cdot 1 \cdot \frac{q_{i}}{N_{i}O_{i}}}} & \ldots & e^{j\; 2{\pi \cdot {({N_{i} - 1})} \cdot \frac{q_{i}}{N_{i}O_{i}}}}\end{bmatrix} \right)}},\mspace{79mu}{0 \leq q_{i} < 0_{i}},{i = {1\mspace{14mu}{or}\mspace{14mu} 2}}} & (11)\end{matrix}$

q₁ and q₂ are assumed to not change, and thus (q₁, q₂) is omitted in thenotation for simplicity. Additionally, B′=[b₀, b₁, . . . , b_(N) ₁ _(N)₂ ₋₁] where b_(i) is the i-th column of the matrix B′ representing thei-th precoding vector.

At 104 a, the present system selects integer indices.

With NR type II CSI codebook, for a candidate pair of (q₁, q₂), the bestL beams (b_(x) ₀ , b_(x) ₁ , . . . , b_(x) _(L-1) ) are selected from B′by Equation (12):

$\begin{matrix}{{\left( {{\hat{x}}_{0},{\hat{x}}_{1},\ldots\;,{\hat{x}}_{L - 1}} \right) = {\arg{\max\limits_{x_{0},x_{1},\;\ldots\;,x_{L - 1}}{M\left( {x_{0},x_{1},\ldots\;,x_{L - 1}} \right)}}}}{{M\left( {x_{0},x_{1},\ldots\;,x_{L - 1}} \right)} = {\sum\limits_{i = 0}^{L - 1}\left( \beta_{x_{i}} \right)^{2}}}} & (12)\end{matrix}$

where β_(i) is defined in Equation (4) and β_(i) for i=0 . . . N₁N₂−1needs to be computed. M(x₀, x₁, . . . , x_(L-1)) is exactly the same asJ({circumflex over (k)}₁,{circumflex over (k)}₂)=J({circumflex over(k)}₁ ⁽⁰⁾, {circumflex over (k)}₂ ⁽⁰⁾, {circumflex over (k)}₁ ⁽¹⁾,{circumflex over (k)}₂ ⁽¹⁾, . . . , {circumflex over (k)}₁ ^((L-1)),{circumflex over (k)}₂ ^((L-1))) calculated in Equation (3) except adifferent index mapping. The L largest elements which maximize themetric can be found by traversing the β_(i) ² array one time with amaximum heap. In full-dimension MIMO (eFD-MIMO), there is a constrainton the distance between the two selected beams and it no longer existsin the new radio (NR) type II channel state information (CSI) codebook.The above integer beam indices selection for NR type II CSI codebook isdifferent for eFD-MIMO.

For eFD-MIMO, the maximization of Equations (3) and (12) for a candidatepair of (q₁, q₂) is can be used to find the first beam with index x andthe second beam with index y that maximize the metric M of Equation (13)and satisfy the second beam selection constraint.

$\begin{matrix}{{\left( {\hat{x},\hat{y}} \right) = {\arg\;{\max\limits_{x,y}{M\left( {x,y} \right)}}}}{{M\left( {x,y} \right)} = \left\{ \begin{matrix}{{\left( \beta_{x} \right)^{2} + \left( \beta_{y} \right)^{2}},} & {{{if}\mspace{14mu}\beta_{y}} \leq \beta_{x}} \\{{\frac{1}{2}\left( {\beta_{x} + \beta_{y}} \right)^{2}},} & {{{if}\mspace{14mu}\beta_{y}} > \beta_{x}}\end{matrix} \right.}} & (13)\end{matrix}$

Equation (13) is subject to Equation (14):mod(y−x,N ₁ N ₂)≤K,K=min(N ₁ ,L ₁)×min(N ₂ ,L ₂)−1  (14)

FIG. 2 is a diagram 200 of a linear complexity method used to findindices x and y, according to an embodiment. First, at 202, the maximumvalue of β_(i) _(max) , 0≤i_(max)<N₁N₂−1 is found. Then, at 204, theleft side local maximum value of β_(i) _(left) , mod(i_(max)−i_(left))≤Kis found. For example, index 210 may be the left side local maximumvalue. Then, at 206, the right side local maximum value of β_(i)_(right) , mod(i_(right)−i_(max))≤K is found. For example, index 212 maybe the right side local maximum value. Then, ½(β_(i) _(left) +β_(i)_(max) )² and (β_(i) _(max) )²+(β_(i) _(right) )² are compared and thelarger one is selected. The corresponding beam indices are (i_(left),i_(max)) or (i_(max), i_(right)).

At 104 b, the present system selects fractional indices. For eachcandidate pair of (q₁, q₂), L beams are found as described above andhave the corresponding maximum value of M denoted as M _(q) ₁ _(,q) ₂ .(q₁, q₂) is selected by Equation (15):

$\begin{matrix}{{\left( {{\overset{\hat{}}{q}}_{1},{\overset{\hat{}}{q}}_{2}} \right) = {\arg\;{\underset{q_{1},q_{2}}{\;\max}{\overset{¯}{M}}_{q_{1\prime}q_{2}}}}},{0 \leq q_{i} < O_{i}},} & (15)\end{matrix}$

The selected integer and fractional indices are mapped to k₁ ^((i)), k₂^((i)) as Equations (16) and (17):

$\begin{matrix}{k_{1}^{(i)} = {{\left\lfloor \frac{x_{i}}{N_{2}} \right\rfloor \cdot O_{1}} + q_{1}}} & (16) \\{k_{2}^{(i)} = {{\left\lfloor {x_{i}\mspace{14mu}\%\mspace{14mu} N_{2}} \right\rfloor \cdot O_{2}} + q_{2}}} & (17)\end{matrix}$

The index operations in Equations (16) and (17) are integer operations,and the % operation represents remainder after division (modulooperation).

At 106, the present system estimates the amplitude and cophasecoefficients based on correlation between the determined precoder andthe selected beams. The cophase coefficients are configured per subbandwhile subband amplitude scaling is optional. p_(r,l,i,k) is denoted asp_(r,l,i,k)={circumflex over (p)}_(r,l,i) ^(WB)·{circumflex over(p)}_(r,l,i,k) ^(SB), {circumflex over (p)}_(r,l,i) ^(WB) is thewideband amplitude scaling factor shared among N_(SB) subbands and{circumflex over (p)}_(r,l,i,k) ^(SB) is for per subband amplitudescaling adjustment.

According to the type II codebook, for each layer the coefficient of thestrongest beam out of 2 L coefficients is 1. Assuming the strongest beamis on the r'-th polarization which is dependent on layer index l andsubband index k, to achieve the above maximum value of J(k₁, k₂), theoptimum solution for cophases c_(r,l,i,k) on the k-th subband isexpressed as Equation (18):

$\begin{matrix}{{\hat{c}}_{r,l,i,k} = \frac{\rho_{r^{\prime},l,0,k}\rho_{r,l,i,k}^{*}}{{\rho_{r^{\prime},l,0,k}\rho_{r,l,i,k}^{*}}}} & (18)\end{matrix}$

and the optimum solutions for {circumflex over (p)}_(r,l,i) ^(WB) and{circumflex over (p)}_(r,l,i,k) ^(SB) are in Equations (19) and (20):

$\begin{matrix}{{\hat{p}}_{r,l,i}^{WB} = \sqrt{\frac{\sum\limits_{k = 0}^{N_{SB} - 1}\rho_{r,l,i,k}^{2}}{\sum\limits_{k = 0}^{N_{SB} - 1}\rho_{r^{\prime},l,0,k}^{2}}}} & (19) \\{{\hat{p}}_{r,l,i,k}^{SB} = \frac{\rho_{r,l,i,k}}{{\rho_{r^{\prime},l,0,k}}{\hat{p}}_{r,l,i}^{WB}}} & (20)\end{matrix}$

Both the cophases and the amplitude scaling factor need to be quantizedbefore feedback and the number of bits are configurable. With L=2, it issimilar to the advanced CSI configuration in LTE eFD-MIMO. The optimumsolution is found as Equations (21) and (22):

$\begin{matrix}{\frac{{\hat{c}}_{r,l,1,k}}{{\hat{c}}_{r,l,0,k}} = \frac{\rho_{r,l,0,k_{mid}}\rho_{r,l,1,k_{mid}}^{*}}{{\rho_{r^{\prime},l,0,k_{mid}}\rho_{r,l,1,k_{mid}}^{*}}}} & (21) \\{\frac{{\hat{p}}_{r,l,1,k}}{{\hat{p}}_{r,l,0,k}} = \frac{\rho_{r,l,1,k_{mid}}}{\rho_{r,l,0,k_{mid}}}} & (22)\end{matrix}$

At 108, alternatively or additionally to 106, the present systemestimates the amplitude and the cophase coefficients by projecting thechannel on the selected base beams. After the beams are selected at 104,the beam selection matrix W₁ is determined as in Equation (23).

$\begin{matrix}{{W_{1} = \begin{bmatrix}B & 0 \\0 & B\end{bmatrix}_{2N_{1}N_{2} \times 2L}},{B = \left\lbrack {b_{k_{1}^{(0)},k_{2}^{(0)}},\ldots\;,b_{k_{1}^{({L - 1})},k_{2}^{({L - 1})}}} \right\rbrack_{N_{1}N_{2} \times L}}} & (23)\end{matrix}$

On the j-th PMI sub-band, the linear combination coefficients (LCCs)estimation problem can be described as in Equation (24).y=H _(j) W ₁ V _(j) x+n  (24)

Given H_(j) and W₁, the system identifies the 2L×N_(Layers) optimal LCCsV_(j). The system projects the channel on the j-th PMI subband H_(j) tothe space of W₁ which is composed of L selected beams on 2polarizations, as in Equation (25).{tilde over (H)} _(j) =H _(j) W ₁ ={tilde over (S)} _(j) {tilde over(D)} _(j) {tilde over (V)} _(j) ^(H)  (25)

The optimum precoding vectors for {tilde over (H)}_(j) are the firstN_(Layers) columns of {tilde over (V)}_(j). With the target precodingvector on the l-th layer of j-th PMI subband defined as V(:,j,l), thenV(:,j,l)={tilde over (V)}_(j)(:,l),l∈[0:N_(Layers)−1]. The SVD operationis performed on the projected channel which has a size of 2L×N_(Rx).This improves the performance and the SVD size is much smaller.

Precoding vectors may be normalized on each subband before applicationat the transmitter (Tx) side, and any scaling or rotation of thefeedback precoding vectors on each subband independently does not affectthe performance. A transform matrix U_(l) can be made to scale and thetarget feedback precoding matrix on the l-th layer V(:,:,l) can berotated while maintaining the same precoding performance. U_(l) is adiagonal matrix with any complex numbers on the diagonal elements, as inEquations (26), (27) and (28).

$\begin{matrix}{{{U_{l}\left( {j,j} \right)}} = {1/{{norm}\left( {V\left( {:{,j,l}} \right)} \right)}}} & (26) \\{{\angle\;{U_{l}\left( {j,j} \right)}} = {\angle\; V\;\left( {1,j,l} \right)}} & (27) \\{{\angle\;{U_{l}\left( {j,j} \right)}} = {{angle}\left( {\sum\limits_{i = 0}^{{2N_{1}N_{1}} - 1}{V\left( {i,j,l} \right)}} \right)}} & (28)\end{matrix}$

Referring back to 102 of FIG. 1, due to hardware limitations, the idealSVD precoder may be determined based on a reduced dimension calculation,such that a 4×4 ED calculation is not required. This can be achieved byapproximating the 4 Rx channel by a 2 Rx channel since the type II CSIonly applies for up to rank 2 cases. The received signal in the timedomain is as Equation (29):

$\begin{matrix}{{Y = {HPx}},{H = \begin{bmatrix}H_{1} \\H_{2}\end{bmatrix}}} & (29)\end{matrix}$

where the size of Y is 4×1, H is 4×16, P is 16×2, x is 2×1, H₁ is 2×16,H₂ is 2×16. A linear combination is used at the receiver side to combinethe 4 Rx channel and get a 2 Rx combined channel as shown in Equation(30):{tilde over (H)}=(W ₁ H ₁ +W ₂ H ₂)P  (30)

The right Eigen vector of {tilde over (H)} can be calculated by 2×2 ED,since {tilde over (H)}{tilde over (H)}^(H) is a 2×2 matrix. The channelH can be approximated by {tilde over (H)} and then the above describedcorrelation based PMI selection can be carried out.

Multiple options exist for selecting W₁ and W₂. First, W₁=U₁ ^(H) andW₂=U₂ ^(H) can be set heuristically with H₁=U₁D₁V₁ ^(H) and H₂=U₂D₂V₂^(H). Second, setting W₁=1 and W₂=0. Third, setting W₁=I and W₂=I.Fourth, selecting the two Rx with the strongest receive power.

FIG. 3 is a block diagram of an electronic device 301 in a networkenvironment 300, according to one embodiment. Referring to FIG. 3, theelectronic device 301 in the network environment 300 may communicatewith an electronic device 302 via a first network 398 (e.g., ashort-range wireless communication network), or an electronic device 304or a server 308 via a second network 399 (e.g., a long-range wirelesscommunication network). The electronic device 301 may communicate withthe electronic device 304 via the server 308. The electronic device 301may include a processor 320, a memory 330, an input device 350, a soundoutput device 355, a display device 360, an audio module 370, a sensormodule 376, an interface 377, a haptic module 379, a camera module 380,a power management module 388, a battery 389, a communication module390, a subscriber identification module (SIM) 396, or an antenna module397. In one embodiment, at least one (e.g., the display device 360 orthe camera module 380) of the components may be omitted from theelectronic device 301, or one or more other components may be added tothe electronic device 301. In one embodiment, some of the components maybe implemented as a single integrated circuit (IC). For example, thesensor module 376 (e.g., a fingerprint sensor, an iris sensor, or anilluminance sensor) may be embedded in the display device 360 (e.g., adisplay).

The processor 320 may execute, for example, software (e.g., a program340) to control at least one other component (e.g., a hardware or asoftware component) of the electronic device 301 coupled with theprocessor 320, and may perform various data processing or computations.As at least part of the data processing or computations, the processor320 may load a command or data received from another component (e.g.,the sensor module 376 or the communication module 390) in volatilememory 332, process the command or the data stored in the volatilememory 332, and store resulting data in non-volatile memory 334. Theprocessor 320 may include a main processor 321 (e.g., a centralprocessing unit (CPU) or an application processor (AP)), and anauxiliary processor 323 (e.g., a graphics processing unit (GPU), animage signal processor (ISP), a sensor hub processor, or a communicationprocessor (CP)) that is operable independently from, or in conjunctionwith, the main processor 321. Additionally or alternatively, theauxiliary processor 323 may be adapted to consume less power than themain processor 321, or execute a particular function. The auxiliaryprocessor 323 may be implemented as being separate from, or a part of,the main processor 321.

The auxiliary processor 323 may control at least some of the functionsor states related to at least one component (e.g., the display device360, the sensor module 376, or the communication module 390) among thecomponents of the electronic device 301, instead of the main processor321 while the main processor 321 is in an inactive (e.g., sleep) state,or together with the main processor 321 while the main processor 321 isin an active state (e.g., executing an application). According to oneembodiment, the auxiliary processor 323 (e.g., an image signal processoror a communication processor) may be implemented as part of anothercomponent (e.g., the camera module 380 or the communication module 390)functionally related to the auxiliary processor 323.

The memory 330 may store various data used by at least one component(e.g., the processor 320 or the sensor module 376) of the electronicdevice 301. The various data may include, for example, software (e.g.,the program 340) and input data or output data for a command relatedthererto. The memory 330 may include the volatile memory 332 or thenon-volatile memory 334.

The program 340 may be stored in the memory 330 as software, and mayinclude, for example, an operating system (OS) 342, middleware 344, oran application 346.

The input device 350 may receive a command or data to be used by othercomponent (e.g., the processor 320) of the electronic device 301, fromthe outside (e.g., a user) of the electronic device 301. The inputdevice 350 may include, for example, a microphone, a mouse, or akeyboard.

The sound output device 355 may output sound signals to the outside ofthe electronic device 301. The sound output device 355 may include, forexample, a speaker or a receiver. The speaker may be used for generalpurposes, such as playing multimedia or recording, and the receiver maybe used for receiving an incoming call. According to one embodiment, thereceiver may be implemented as being separate from, or a part of, thespeaker.

The display device 360 may visually provide information to the outside(e.g., a user) of the electronic device 301. The display device 360 mayinclude, for example, a display, a hologram device, or a projector andcontrol circuitry to control a corresponding one of the display,hologram device, and projector. According to one embodiment, the displaydevice 360 may include touch circuitry adapted to detect a touch, orsensor circuitry (e.g., a pressure sensor) adapted to measure theintensity of force incurred by the touch.

The audio module 370 may convert a sound into an electrical signal andvice versa. According to one embodiment, the audio module 370 may obtainthe sound via the input device 350, or output the sound via the soundoutput device 355 or a headphone of an external electronic device 302directly (e.g., wiredly) or wirelessly coupled with the electronicdevice 301.

The sensor module 376 may detect an operational state (e.g., power ortemperature) of the electronic device 301 or an environmental state(e.g., a state of a user) external to the electronic device 301, andthen generate an electrical signal or data value corresponding to thedetected state. The sensor module 376 may include, for example, agesture sensor, a gyro sensor, an atmospheric pressure sensor, amagnetic sensor, an acceleration sensor, a grip sensor, a proximitysensor, a color sensor, an infrared (IR) sensor, a biometric sensor, atemperature sensor, a humidity sensor, or an illuminance sensor.

The interface 377 may support one or more specified protocols to be usedfor the electronic device 301 to be coupled with the external electronicdevice 302 directly (e.g., wiredly) or wirelessly. According to oneembodiment, the interface 377 may include, for example, a highdefinition multimedia interface (HDMI), a universal serial bus (USB)interface, a secure digital (SD) card interface, or an audio interface.

A connecting terminal 378 may include a connector via which theelectronic device 301 may be physically connected with the externalelectronic device 302. According to one embodiment, the connectingterminal 378 may include, for example, an HDMI connector, a USBconnector, an SD card connector, or an audio connector (e.g., aheadphone connector).

The haptic module 379 may convert an electrical signal into a mechanicalstimulus (e.g., a vibration or a movement) or an electrical stimuluswhich may be recognized by a user via tactile sensation or kinestheticsensation. According to one embodiment, the haptic module 379 mayinclude, for example, a motor, a piezoelectric element, or an electricalstimulator.

The camera module 380 may capture a still image or moving images.According to one embodiment, the camera module 380 may include one ormore lenses, image sensors, image signal processors, or flashes.

The power management module 388 may manage power supplied to theelectronic device 301. The power management module 388 may beimplemented as at least part of, for example, a power managementintegrated circuit (PMIC).

The battery 389 may supply power to at least one component of theelectronic device 301. According to one embodiment, the battery 389 mayinclude, for example, a primary cell which is not rechargeable, asecondary cell which is rechargeable, or a fuel cell.

The communication module 390 may support establishing a direct (e.g.,wired) communication channel or a wireless communication channel betweenthe electronic device 301 and the external electronic device (e.g., theelectronic device 302, the electronic device 304, or the server 308) andperforming communication via the established communication channel. Thecommunication module 390 may include one or more communicationprocessors that are operable independently from the processor 320 (e.g.,the AP) and supports a direct (e.g., wired) communication or a wirelesscommunication. According to one embodiment, the communication module 390may include a wireless communication module 392 (e.g., a cellularcommunication module, a short-range wireless communication module, or aglobal navigation satellite system (GNSS) communication module) or awired communication module 394 (e.g., a local area network (LAN)communication module or a power line communication (PLC) module). Acorresponding one of these communication modules may communicate withthe external electronic device via the first network 398 (e.g., ashort-range communication network, such as Bluetooth™, wireless-fidelity(Wi-Fi) direct, or a standard of the Infrared Data Association (IrDA))or the second network 399 (e.g., a long-range communication network,such as a cellular network, the Internet, or a computer network (e.g.,LAN or wide area network (WAN)). These various types of communicationmodules may be implemented as a single component (e.g., a single IC), ormay be implemented as multiple components (e.g., multiple ICs) that areseparate from each other. The wireless communication module 392 mayidentify and authenticate the electronic device 301 in a communicationnetwork, such as the first network 398 or the second network 399, usingsubscriber information (e.g., international mobile subscriber identity(IMSI)) stored in the subscriber identification module 396.

The antenna module 397 may transmit or receive a signal or power to orfrom the outside (e.g., the external electronic device) of theelectronic device 301. According to one embodiment, the antenna module397 may include one or more antennas, and, therefrom, at least oneantenna appropriate for a communication scheme used in the communicationnetwork, such as the first network 398 or the second network 399, may beselected, for example, by the communication module 390 (e.g., thewireless communication module 392). The signal or the power may then betransmitted or received between the communication module 390 and theexternal electronic device via the selected at least one antenna.

At least some of the above-described components may be mutually coupledand communicate signals (e.g., commands or data) therebetween via aninter-peripheral communication scheme (e.g., a bus, a general purposeinput and output (GPIO), a serial peripheral interface (SPI), or amobile industry processor interface (MIPI)).

According to one embodiment, commands or data may be transmitted orreceived between the electronic device 301 and the external electronicdevice 304 via the server 308 coupled with the second network 399. Eachof the electronic devices 302 and 304 may be a device of a same type as,or a different type, from the electronic device 301. All or some ofoperations to be executed at the electronic device 301 may be executedat one or more of the external electronic devices 302, 304, or 308. Forexample, if the electronic device 301 should perform a function or aservice automatically, or in response to a request from a user oranother device, the electronic device 301, instead of, or in additionto, executing the function or the service, may request the one or moreexternal electronic devices to perform at least part of the function orthe service. The one or more external electronic devices receiving therequest may perform the at least part of the function or the servicerequested, or an additional function or an additional service related tothe request, and transfer an outcome of the performing to the electronicdevice 301. The electronic device 301 may provide the outcome, with orwithout further processing of the outcome, as at least part of a replyto the request. To that end, a cloud computing, distributed computing,or client-server computing technology may be used, for example.

One embodiment may be implemented as software (e.g., the program 340)including one or more instructions that are stored in a storage medium(e.g., internal memory 336 or external memory 338) that is readable by amachine (e.g., the electronic device 301). For example, a processor ofthe electronic device 301 may invoke at least one of the one or moreinstructions stored in the storage medium, and execute it, with orwithout using one or more other components under the control of theprocessor. Thus, a machine may be operated to perform at least onefunction according to the at least one instruction invoked. The one ormore instructions may include code generated by a complier or codeexecutable by an interpreter. A machine-readable storage medium may beprovided in the form of a non-transitory storage medium. The term“non-transitory” indicates that the storage medium is a tangible device,and does not include a signal (e.g., an electromagnetic wave), but thisterm does not differentiate between where data is semi-permanentlystored in the storage medium and where the data is temporarily stored inthe storage medium.

According to one embodiment, a method of the disclosure may be includedand provided in a computer program product. The computer program productmay be traded as a product between a seller and a buyer. The computerprogram product may be distributed in the form of a machine-readablestorage medium (e.g., a compact disc read only memory (CD-ROM)), or bedistributed (e.g., downloaded or uploaded) online via an applicationstore (e.g., Play Store™), or between two user devices (e.g., smartphones) directly. If distributed online, at least part of the computerprogram product may be temporarily generated or at least temporarilystored in the machine-readable storage medium, such as memory of themanufacturer's server, a server of the application store, or a relayserver.

According to one embodiment, each component (e.g., a module or aprogram) of the above-described components may include a single entityor multiple entities. One or more of the above-described components maybe omitted, or one or more other components may be added. Alternativelyor additionally, a plurality of components (e.g., modules or programs)may be integrated into a single component. In this case, the integratedcomponent may still perform one or more functions of each of theplurality of components in the same or similar manner as they areperformed by a corresponding one of the plurality of components beforethe integration. Operations performed by the module, the program, oranother component may be carried out sequentially, in parallel,repeatedly, or heuristically, or one or more of the operations may beexecuted in a different order or omitted, or one or more otheroperations may be added.

Although certain embodiments of the present disclosure have beendescribed in the detailed description of the present disclosure, thepresent disclosure may be modified in various forms without departingfrom the scope of the present disclosure. Thus, the scope of the presentdisclosure shall not be determined merely based on the describedembodiments, but rather determined based on the accompanying claims andequivalents thereto.

What is claimed is:
 1. A method for selecting precoding matrix index(PMI), comprising: determining a precoder and candidate beams; selectingbase beams based on a correlation power between the determined precoderand determined candidate beams; and estimating amplitude coefficientsand cophase coefficients by projecting a channel on the selected basebeams.
 2. The method of claim 1, wherein the precoder is determined by areduced dimension singular value decomposition (SVD).
 3. The method ofclaim 2, wherein the reduced dimension SVD reduces the precoderdetermination from a 4×4 SVD calculation to a 2×2 SVD calculation. 4.The method of claim 1, wherein selecting base beams further comprisesselecting integer indices.
 5. The method of claim 4, wherein selectinginteger indices is based on linear complexity in a multiple inputmultiple output (MIMO) system.
 6. The method of claim 1, whereinselecting base beams further comprises selecting fractional indices. 7.The method of claim 1, wherein the estimating the amplitude and cophasecoefficients is based on a wide band amplitude scaling factor{circumflex over (p)}_(r,l,i) ^(WB) and a per subband amplitude scalingadjustment factor {circumflex over (p)}_(r,l,i,k) ^(SB).
 8. The methodof claim 1, wherein the projecting the channel on the selected basebeams comprises identifying optimal linear combination coefficients(LCCs).
 9. The method of claim 1, wherein the projecting the channel onthe selected base beams comprises projecting the channel on a j-th PMIsubband to a space of a beam selection matrix.
 10. The method of claim9, wherein the projecting the channel on the j-th PMI subband to thespace of the beam selection matrix comprises determining optimumprecoding vectors.
 11. A system for selecting precoding matrix index(PMI), comprising: a transmitter; a receiver; and a processor configuredto: determine a precoder and candidate beams; select base beams based ona correlation power between the determined precoder and determinedcandidate beams; and estimate amplitude coefficients and cophasecoefficients by projecting a channel on the selected base beams.
 12. Thesystem of claim 11, wherein the processor is configured to determine theprecoder by a reduced dimension singular value decomposition (SVD). 13.The system of claim 12, wherein the reduced dimension SVD reduces theprecoder determination from a 4×4 SVD calculation to a 2×2 SVDcalculation.
 14. The system of claim 11, wherein the processor isfurther configured to select base beams by selecting integer indices.15. The system of claim 14, wherein the processor is further configuredto select integer indices based on linear complexity in a multiple inputmultiple output (MIMO) system.
 16. The system of claim 11, wherein theprocessor is further configured to select base beams by selectingfractional indices.
 17. The system of claim 11, wherein the processor isfurther configured to estimate the amplitude and cophase coefficientsbased on a wide band amplitude scaling factor {circumflex over(p)}_(r,l,i) ^(WB) and a per subband amplitude scaling adjustment factor{circumflex over (p)}_(r,l,i,k) ^(SB).
 18. The system of claim 11,wherein the projecting the channel on the selected base beams comprisesidentifying optimal linear combination coefficients (LCCs).
 19. Thesystem of claim 11, wherein the projecting the channel on the selectedbase beams comprises projecting the channel on a j-th PMI subband to aspace of a beam selection matrix.
 20. The system of claim 19, whereinthe projecting the channel on the j-th PMI subband to the space of thebeam selection matrix comprises determining optimum precoding vector.